1. Surface Area of Prisms and Cylinders Retrieved from http://www.mrhammond.org/math/mathlessons/http://www.mrhammond.org/math/mathlessons/

2. Vocabulary A net is a pattern you can fold to form a three-dimensional figure. This is a net for a triangular prism.

3. The surface area of a three- dimensional figure is the sum of the areas of its surfaces. Find the area of each surface, and add all the areas together.

4. Example 1 26 cm 8 cm 18 cm Triangles A = ½ bh A = ½ (26)(18) A = ½ (468) A = 234 cm 2 2 Tri’s: 234 x 2 = 468 cm 2 Left Rectangle A = lw A = (18)(8) A = 144 cm 2 Front and Back Rectangles A = lw A = (26)(8) A = 208 cm 2 2 Rect’s: 208 x 2 = 416 cm 2

5. Add up the areas to find surface area. S.A. = 468 cm 2 + 144 cm 2 + 416 cm 2 S.A. = 1,028 cm 2

6. Surface Area of a Cube A cube has 6 congruent square faces. Find the area of one face, and multiply it by 6.

7. Example 7 in A = s 2 A = 7 2 A = 49 in 2 S.A. = 49(6) S.A. = 294 in 2

8. Surface Area of a Rectangular Prism The surface area of a rectangular prism is the area of the six rectangles that cover it. To find the surface area, we don't have to figure out all six because we know that the top and bottom (length x width) are the same, the front and back (length x height) are the same, and the left and right sides (width x height) are the same. So, we can use the formula SA = 2(lh) + 2(lw) + 2(wh)

9. Surface Area of a Rectangular Prism 10 cm 7 cm 6 cm SA = 2(lh) + 2(lw) + 2(wh) SA = 2(6cm x 10cm) + 2(6cm x 7cm) + 2(7cm x 10cm) SA = 2(60cm²) + 2(42cm²) + (70cm²) SA = 120cm² + 84cm² + 140cm² SA = 344cm²

10. Surface Area of a Cylinder A cylinder consists of two circle bases and one rectangular side. The length of the rectangle is equal to the circumference of the circle. Find the area of the circles and add it to the area of the rectangle.

11. Example 5 m 16 m Area of the circles A =  r 2 A = 3.14(5 2 ) A = 3.14 (25) A = 78.5 m 2 2 circles: 78.5 x 2 = 157 m 2 Rectangle The width of the rectangle is the height of the cylinder (16 m). The length of the rectangle is the circumference of the circle. C = 2  r C = 2(3.14)(5) C = 31.4 m A = lw A = 31.4(16) A = 502.4 m 2

12. Put the areas together: S.A. = 157 m 2 + 502.4 m 2 S.A. = 659.4 m 2

13. Homework Time